Dynamic p-enrichment schemes for multicomponent reactive flows

Abstract

We present a family of p-enrichment schemes. These schemes may be separated into two basic classes: the first, called fixed tolerance schemes, rely on setting global scalar tolerances on the local regularity of the solution, and the second, called dioristic schemes, rely on time-evolving bounds on the local variation in the solution. Each class of p-enrichment scheme is further divided into two basic types. The first type (the Type I schemes) enrich along lines of maximal variation, striving to enhance stable solutions in “areas of highest interest.” The second type (the Type II schemes) enrich along lines of maximal regularity in order to maximize the stability of the enrichment process. Each of these schemes are tested on three model systems. The first is an academic exact system where basic analysis is easily performed. Then we discuss a pair of application model problems arising in coastal hydrology. The first being a contaminant transport model, which addresses a declinature problem for a contaminant plume with respect to a bay inlet setting. And the second, a multicomponent chemically reactive flow model of estuary eutrophication arising in the Gulf of Mexico.